Metodología de análisis estadístico de roturas en redes de distribución de agua

La presente Tesis plantea una metodología de análisis estadístico de roturas de tubería en redes de distribución de agua, que analiza la relación entre las roturas y la presión de agua y que propone la implantación de una gestión de presiones que reduzca el número de roturas que se producen en dichas redes. Las redes de distribución de agua se deterioran y una de sus graves consecuencias es la aparición de roturas frecuentes en sus tuberías. Las roturas llevan asociados elevados costes sociales, económicos y medioambientales y es por ello por lo que las compañías gestoras del agua tratan de reducirlas en la medida de lo posible. Las redes de distribución de agua se pueden dividir en zonas o sectores que facilitan su control y que pueden ser independientes o aislarse mediante válvulas, como ocurre en las redes de países más desarrollados, o pueden estar intercomunicados hidráulicamente. La implantación de una gestión de presiones suele llevarse a cabo a través de las válvulas reductoras de presión (VPR), que se instalan en las cabeceras de estos sectores y que controlan la presión aguas abajo de la misma, aunque varíe su caudal de entrada. Los métodos más conocidos de la gestión de presiones son la reducción de presiones, que es el control más habitual, el mantenimiento de la presión, la prevención y/o alivio de los aumentos repentinos de presión y el establecimiento de un control por alturas. A partir del año 2005 se empezó a reconocer el efecto de la gestión de presiones sobre la disminución de las roturas. En esta Tesis, se sugiere una gestión de presiones que controle los rangos de los indicadores de la presión de cabecera que más influyan en la probabilidad de roturas de tubería. Así, la presión del agua se caracteriza a través de indicadores obtenidos de la presión registrada en la cabecera de los sectores, debido a que se asume que esta presión es representativa de la presión de operación de todas las tuberías porque las pérdidas de carga son relativamente bajas y las diferencias topográficas se tienen en cuenta en el diseño de los sectores. Y los indicadores de presión, que se pueden definir como el estadístico calculado a partir de las series de la presión de cabecera sobre una ventana de tiempo, pueden proveer la información necesaria para ayudar a la toma de decisiones a los gestores del agua con el fin de reducir las roturas de tubería en las redes de distribución de agua. La primera parte de la metodología que se propone en esta Tesis trata de encontrar los indicadores de presión que influyen más en la probabilidad de roturas de tuberías. Para conocer si un indicador es influyente en la probabilidad de las roturas se comparan las estimaciones de las funciones de distribución acumulada (FDAs) de los indicadores de presiones, considerando dos situaciones: cuando se condicionan a la ocurrencia de una rotura (suceso raro) y cuando se calculan en la situación normal de operación (normal operación). Por lo general, las compañías gestoras cuentan con registros de roturas de los años más recientes y al encontrarse las tuberías enterradas se complica el acceso a la información. Por ello, se propone el uso de funciones de probabilidad que permiten reducir la incertidumbre asociada a los datos registrados. De esta forma, se determinan las funciones de distribución acumuladas (FDAs) de los valores del indicador de la serie de presión (situación normal de operación) y las FDAs de los valores del indicador en el momento de ocurrencia de las roturas (condicionado a las roturas). Si las funciones de distribución provienen de la misma población, no se puede deducir que el indicador claramente influya en la probabilidad de roturas. Sin embargo, si se prueba estadísticamente que las funciones proceden de la misma población, se puede concluir que existe una relación entre el indicador analizado y la ocurrencia de las roturas. Debido a que el número de valores del indicador de la FDA condicionada a las roturas es mucho menor que el número de valores del indicador de la FDA incondicional a las roturas, se generan series aleatorias a partir de los valores de los indicadores con el mismo número de valores que roturas registradas hay. De esta forma, se comparan las FDAs de series aleatorias del indicador con la FDA condicionada a las roturas del mismo indicador y se deduce si el indicador es influyente en la probabilidad de las roturas. Los indicadores de presión pueden depender de unos parámetros. A través de un análisis de sensibilidad y aplicando un test estadístico robusto se determina la situación en la que estos parámetros dan lugar a que el indicador sea más influyente en la probabilidad de las roturas. Al mismo tiempo, los indicadores se pueden calcular en función de dos parámetros de cálculo que se denominan el tiempo de anticipación y el ancho de ventana. El tiempo de anticipación es el tiempo (en horas) entre el final del periodo de computación del indicador de presión y la rotura, y el ancho de ventana es el número de valores de presión que se requieren para calcular el indicador de presión y que es múltiplo de 24 horas debido al comportamiento cíclico diario de la presión. Un análisis de sensibilidad de los parámetros de cálculo explica cuándo los indicadores de presión influyen más en la probabilidad de roturas. En la segunda parte de la metodología se presenta un modelo de diagnóstico bayesiano. Este tipo de modelo forma parte de los modelos estadísticos de prevención de roturas, parten de los datos registrados para establecer patrones de fallo y utilizan el teorema de Bayes para determinar la probabilidad de fallo cuando se condiciona la red a unas determinadas características. Así, a través del teorema de Bayes se comparan la FDA genérica del indicador con la FDA condicionada a las roturas y se determina cuándo la probabilidad de roturas aumenta para ciertos rangos del indicador que se ha inferido como influyente en las roturas. Se determina un ratio de probabilidad (RP) que cuando es superior a la unidad permite distinguir cuándo la probabilidad de roturas incrementa para determinados intervalos del indicador. La primera parte de la metodología se aplica a la red de distribución de la Comunidad de Madrid (España) y a la red de distribución de Ciudad de Panamá (Panamá). Tras el filtrado de datos se deduce que se puede aplicar la metodología en 15 sectores en la Comunidad de Madrid y en dos sectores, llamados corregimientos, en Ciudad de Panamá. Los resultados demuestran que en las dos redes los indicadores más influyentes en la probabilidad de las roturas son el rango de la presión, que supone la diferencia entre la presión máxima y la presión mínima, y la variabilidad de la presión, que considera la propiedad estadística de la desviación típica. Se trata, por tanto, de indicadores que hacen referencia a la dispersión de los datos, a la persistencia de la variación de la presión y que se puede asimilar en resistencia de materiales a la fatiga. La segunda parte de la metodología se ha aplicado a los indicadores influyentes en la probabilidad de las roturas de la Comunidad de Madrid y se ha deducido que la probabilidad de roturas aumenta para valores extremos del indicador del rango de la presión y del indicador de la variabilidad de la presión. Finalmente, se recomienda una gestión de presiones que limite los intervalos de los indicadores influyentes en la probabilidad de roturas que incrementen dicha probabilidad. La metodología propuesta puede aplicarse a otras redes de distribución y puede ayudar a las compañías gestoras a reducir el número de fallos en el sistema a través de la gestión de presiones. This Thesis presents a methodology for the statistical analysis of pipe breaks in water distribution networks. The methodology studies the relationship between pipe breaks and water pressure, and proposes a pressure management procedure to reduce the number of breaks that occur in such networks. One of the manifestations of the deterioration of water supply systems is frequent pipe breaks. System failures are one of the major challenges faced by water utilities, due to their associated social, economic and environmental costs. For all these reasons, water utilities aim at reducing the problem of break occurrence to as great an extent as possible. Water distribution networks can be divided into areas or sectors, which facilitates the control of the network. These areas may be independent or isolated by valves, as it usually happens in developing countries. Alternatively, they can be hydraulically interconnected. The implementation of pressure management strategies is usually carried out through pressure-reducing valves (PRV). These valves are installed at the head of the sectors and, although the inflow may vary significantly, they control the downstream pressure. The most popular methods of pressure management consist of pressure reduction, which is the common form of control, pressure sustaining, prevention and/or alleviation of pressure surges or large variations in pressure, and level/altitude control. From 2005 onwards, the effects of pressure management on burst frequencies have become more widely recognized in the technical literature. This thesis suggests a pressure management that controls the pressure indicator ranges most influential on the probability of pipe breaks. Operating pressure in a sector is characterized by means of a pressure indicator at the head of the DMA, as head losses are relatively small and topographical differences were accounted for at the design stage. The pressure indicator, which may be defined as the calculated statistic from the time series of pressure head over a specific time window, may provide necessary information to help water utilities to make decisions to reduce pipe breaks in water distribution networks. The first part of the methodology presented in this Thesis provides the pressure indicators which have the greatest impact on the probability of pipe breaks to be determined. In order to know whether a pressure indicator influences the probability of pipe breaks, the proposed methodology compares estimates of cumulative distribution functions (CDFs) of a pressure indicator through consideration of two situations: when they are conditioned to the occurrence of a pipe break (a rare event), and when they are not (a normal operation). Water utilities usually have a history of failures limited to recent periods of time, and it is difficult to have access to precise information in an underground network. Therefore, the use of distribution functions to address such imprecision of recorded data is proposed. Cumulative distribution functions (CDFs) derived from the time series of pressure indicators (normal operation) and CDFs of indicator values at times coincident with a reported pipe break (conditioned to breaks) are compared. If all estimated CDFs are drawn from the same population, there is no reason to infer that the studied indicator clearly influences the probability of the rare event. However, when it is statistically proven that the estimated CDFs do not come from the same population, the analysed indicator may have an influence on the occurrence of pipe breaks. Due to the fact that the number of indicator values used to estimate the CDF conditioned to breaks is much lower in comparison with the number of indicator values to estimate the CDF of the unconditional pressure series, and that the obtained results depend on the size of the compared samples, CDFs from random sets of the same size sampled from the unconditional indicator values are estimated. Therefore, the comparison between the estimated CDFs of random sets of the indicator and the estimated CDF conditioned to breaks allows knowledge of if the indicator is influential on the probability of pipe breaks. Pressure indicators depend on various parameters. Sensitivity analysis and a robust statistical test allow determining the indicator for which these parameters result most influential on the probability of pipe breaks. At the same time, indicators can be calculated according to two model parameters, named as the anticipation time and the window width. The anticipation time refers to the time (hours) between the end of the period for the computation of the pressure indicator and the break. The window width is the number of instantaneous pressure values required to calculate the pressure indicator and is multiple of 24 hours, as water pressure has a cyclical behaviour which lasts one day. A sensitivity analysis of the model parameters explains when the pressure indicator is more influential on the probability of pipe breaks. The second part of the methodology presents a Bayesian diagnostic model. This kind of model belongs to the class of statistical predictive models, which are based on historical data, represent break behavior and patterns in water mains, and use the Bayes’ theorem to condition the probability of failure to specific system characteristics. The Bayes’ theorem allows comparing the break-conditioned FDA and the unconditional FDA of the indicators and determining when the probability of pipe breaks increases for certain pressure indicator ranges. A defined probability ratio provides a measure to establish whether the probability of breaks increases for certain ranges of the pressure indicator. The first part of the methodology is applied to the water distribution network of Madrid (Spain) and to the water distribution network of Panama City (Panama). The data filtering method suggests that the methodology can be applied to 15 sectors in Madrid and to two areas in Panama City. The results show that, in both systems, the most influential indicators on the probability of pipe breaks are the pressure range, which is the difference between the maximum pressure and the minimum pressure, and pressure variability, referred to the statistical property of the standard deviation. Therefore, they represent the dispersion of the data, the persistence of the variation in pressure and may be related to the fatigue in material resistance. The second part of the methodology has been applied to the influential indicators on the probability of pipe breaks in the water distribution network of Madrid. The main conclusion is that the probability of pipe breaks increases for the extreme values of the pressure range indicator and of the pressure variability indicator. Finally, a pressure management which limits the ranges of the pressure indicators influential on the probability of pipe breaks that increase such probability is recommended. The methodology presented here is general, may be applied to other water distribution networks, and could help water utilities reduce the number of system failures through pressure management.

High precision pressure sensors based on SAW devices in the GHz range

In this paper, an AlN/free-standing nanocrystalline diamond (NCD) system is proposed in order to process high frequency surface acoustic wave (SAW) resonators for sensing applications. The main problem of synthetic diamond is its high surface roughness that worsens the sputtered AlN quality and hence the device response. In order to study the feasibility of this structure, AlN films from 150 nm up to 1200 nm thick have been deposited on free-standing NCD. We have then analysed the influence of the AlN layer thickness on its crystal quality and device response. Optimized thin films of 300 nm have been used to fabricate of one-port SAW resonators operating in the 10–14 GHz frequency range. A SAW based sensor pressure with a sensibility of 0.33 MHz/bar has been fabricated.

Pressure measurements of the detachment bubble on the Bolund Island

Pressure measurements on the surface of a 1:230 scale model of Bolund Island are presented. The model is smooth and no boundary layer generation has been considered since the experiment is designed as the simplest possible reference case. Measurement have been taken for a range of Reynolds numbers based on the average undisturbed wind speed U∞ and the maximum height of the island, h [1.7×104, 8.5×104], and for a range of wind directions. Four minutes time series of pressure in more than 400 points have been acquired and analysed to obtain the spatial distribution of both the time average and the variance of the pressure signal. The horizontal extension of the detachment bubble for the different Reynolds numbers and wind directions is identified by isobars and curves of constant value of pressure variance. The applicability of this technique for evaluating the horizontal topology of high turbulence regions associated to detachment bubbles after escarpments in potential wind farm sites is analysed. The results obtained shows that the behaviour of the mean pressure coefficient, Cp, the std. pressure coefficient, Cp, and the skewness of the pressure, Sp can be used to study the bubble over the island to a certain extent. This experiment is part of the set of different analysis on the Bolund test case that is being undertaken within WAUDIT project by the different scientific groups.

Performance of pressure control valves and flow meters precision in operational irrigation-water balance accuracy

In pressure irrigation-water distribution networks, pressure regulating devices for controlling the discharged flow rate by irrigation units are needed due to the variability of flow rate. In addition, applied water volume is used controlled operating the valve during a calculated time interval, and assuming constant flow rate. In general, a pressure regulating valve PRV is the commonly used pressure regulating device in a hydrant, which, also, executes the open and close function. A hydrant feeds several irrigation units, requiring a wide range in flow rate. In addition, some flow meters are also available, one as a component of the hydrant and the rest are placed downstream. Every land owner has one flow meter for each group of field plots downstream the hydrant. Its lecture could be used for refining the water balance but its accuracy must be taken into account. Ideal PRV performance would maintain a constant downstream pressure. However, the true performance depends on both upstream pressure and the discharged flow rate. The objective of this work is to asses the influence of the performance on the applied volume during the whole irrigation events in a year. The results of the study have been obtained introducing the flow rate into a PRV model. Variations on flow rate are simulated by taking into account the consequences of variations on climate conditions and also decisions in irrigation operation, such us duration and frequency application. The model comprises continuity, dynamic and energy equations of the components of the PRV.

Pressure measurements of the detachment bubble on the Bolund Island

Pressure measurements on the surface of a 1:230 scale model of Bolund Island are presented. The model is smooth and no boundary layer generation has been considered since the experiment is designed as the simplest possible reference case. Measurement have been taken for a range of Reynolds numbers based on the average undisturbed wind speed U? and the maximum height of the island, h [1.7×104 , 8.5×104], and for a range of wind directions. Four minutes time series of pressure in more than 400 points have been acquired and analysed to obtain the spatial distribution of both the time average and the variance of the pressure signal. The horizontal extension of the detachment bubble for the different Reynolds numbers and wind directions is identified by isobars and curves of constant value of pressure variance. The applicability of this technique for evaluating the horizontal topology of high turbulence regions associated to detachment bubbles after escarpments in potential wind farm sites is analysed. The results obtained shows that the behaviour of the mean pressure coefficient, Cp, the std. pressure coefficient, C?p, and the skewness of the pressure, Sp can be used to study the bubble over the island to a certain extent. This experiment is part of the set of different analysis on the Bolund test case that is being undertaken within WAUDIT project by the different scientific groups.

Effect of composition, sonication and pressure on the rate capability of 5 V-LiNi0.5Mn1.5O4 composite cathodes

Positive composite electrodes having LiNi0.5Mn1.5O4 spinel as active material, a blend of graphite and carbon black for increasing the electrode electrical conductivity and either polyvinyldenefluoride (PVDF) or a blend of PVDF with a small amount of Teflon® (1 wt%) for building up the electrode. They have been processed by tape casting on an aluminum foil as current collector using the doctor blade technique. Additionally, the component blends were either sonicated or not, and the processed electrodes were compacted or not under subsequent cold pressing. Composites electrodes with high weight, up to 17 mg/cm2, were prepared and studied as positive electrodes for lithium-ion batteries. The addition of Teflon® and the application of the sonication treatment lead to uniform electrodes that are well-adhered to the aluminum foil. Both parameters contribute to improve the capacity drained at high rates (5C). Additional compaction of the electrode/aluminum assemblies remarkably enhances the electrode rate capabilities. At 5C rate, remarkable capacity retentions between 80% and 90% are found for electrodes with weights in the range 3–17 mg/cm2, having Teflon® in their formulation, prepared after sonication of their component blends and compacted under 2 tonnes/cm2.